Format and topics for final exam
General information. The final exam will be a comprehensive timed exam, held Fri May 17, 12:15pm-2:30pm, in our usual classroom. The test will cover all of the material on the three in-class midterms, as well as sections 5.3, 5.5, and 6.1-6.2 of the text. No books, notes, calculators, etc., are allowed. Most of the exam will rely on understanding the problem sets (including problems to be done but not to be turned in), the quizzes, and the definitions and theorems that lie behind them. If you can do all of the homework and the quizzes, and you know and understand all of the definitions and the statements of all of the theorems we've studied, you should be in good shape.
You should not spend time memorizing proofs of theorems from the book, but you should defintely spend time memorizing the statements of the important theorems in the text, especially any named theorems.
Types of questions. The final exam will include the usual computations, statements of definitions and theorems, true/false with justification, and paragraph-style questions.
Definitions. The most important definitions and symbols we have covered are:
5.3 diagonalizable D, P notation 5.5 Markov chain states of a Markov chain transition matrix regular Markov chain differential equation general solution initial condition particular solution 6.1 norm (length) of v ||v|| distance between u and v dot product u·v orthogonal (perpendicular) orthogonal projection of v onto a line 6.2 orthogonal set orthogonal basis unit vector orthonormal basis orthogonal complement Wperp orthogonal projection of v onto W distance from v to W
Examples. Make sure you understand the following examples.
Theorems, results, algorithms. The most important theorems, results, and algorithms we have covered are listed below. You should understand all of these results, and you should be able to cite them as needed. You should also be prepared to recite named theorems.
Types of computations. You should also know how to do the following general types of computations. (Note also that on the actual exam, there will be problems that are not of these types. Nevertheless, it will be helpful to know how to do all these types.)
Not on exam. Section 5.5: Harmonic motion, difference equations. Section 6.1: Cauchy-Schwartz inequality, triangle inequality.